Choosing one kind of type system into use excludes the other kind of type systems since the whole thing needs to be consistent. Type level lambda would be very strange in category theory...
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tp1Dec 1 '12 at 9:29

1 Answer
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Type inference with type level lambdas would require higher order unification which is undecidable. This is the motivation for disallowing them. But as has happened with other undecidable features (like type inference for GADTs), it might be possible to require type signatures and allow it. I'm not sure if that's been investigated by anyone.